Finite Group Databasebeta

C3×#15691680 #23748542

order9477
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C36

Aliases

direct productC3×#15691680

Splittings

FittingC3×C13×#733 ⋊ C3
SylowC13 ⋊ C3×#6913

Subgroups

subgroupG/H
centerC32H(3,𝔽3)×C13⋊C3
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC3×C13×#733C3
socleC32×C13C3×H(3,𝔽3)
hypercenterC3×#733C13⋊C3
hypocenterC13C3×#6913
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C32 ◁ C33 ◁ C3×#733

992 conjugacy classes of subgroups; only the 274 normal subgroups are shown.

normal subgroups only

This group has 992 conjugacy classes of subgroups — too many to draw. Only its 274 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

309 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9477, 3951);